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February 28th, 2022 (Permalink)

Putin, Trudeau & Jewish Nazis

The biggest news in the last week is, of course, Russia invading Ukraine. The dictator of Russia, Vladimir Putin, is attempting to justify the invasion by accusing the Ukrainians of being neo-Nazis. This month's Recommended Reading will focus on Putin's propaganda, together with disturbingly similar rhetoric from closer to home.


  1. Michael E. Ruane, "Putin’s attack on Ukraine echoes Hitler’s takeover of Czechoslovakia", The Washington Post, 2/24/2022
  2. George Orwell, "What is Fascism?", Tribune, 1944
  3. Patrick J. Kiger, "How Joseph Stalin Starved Millions in the Ukrainian Famine", History, 4/16/2019
  4. I've edited this quote based on the following article: Kenneth Garger, "Justin Trudeau sparks outrage after accusing Jewish conservatives of supporting swastikas", New York Post, 2/16/2022
  5. "Ottawa Police Investigating Some Anti Vaccine Protesters", Associated Press, 1/30/2022
  6. Lora Korpar, "Freedom Convoy Leader Tamara Lich Denied Bail After Arrest in Ottawa", Newsweek, 2/22/2022
  7. Jordan Liles, "Swastikas and Confederate Flags Seen at Canada’s ‘Freedom Convoy’", Snopes, 2/17/2022

Disclaimer: I don't necessarily agree with everything in these articles, but I think they're worth reading as a whole.

February 21st, 2022 (Permalink)

A Tendentious Top Ten

The Pfizer-BioNTech vaccine against COVID-19 was not approved for use in children under the age of twelve until October 29th of last year, when it was approved for those aged 5-11 in a reduced dosage1. At a press conference a couple of days earlier, the director of the Centers for Disease Control and Prevention, Rochelle Walensky, said the following:

Understanding where we are in the current state of the pandemic allows us to look forward to what is on the horizon and to be clear in our efforts…. This includes protecting our children and understanding the risk that COVID-19 poses to them. The health and wellbeing of our nation’s children is of the utmost importance. …[T]he regulatory process is underway to make COVID-19 vaccines available for children ages 5 to 11. And I’d like to just step back and take a moment to put some of this into perspective. CDC’s data presented at yesterday’s FDA Advisory Committee showed that among all children ages 5 to 11, COVID-19 was one of the top 10 causes of death in the United States over the last year.2

Why did Walensky make this "top ten" claim? As mentioned above, she made it during a press conference anticipating the approval of the vaccine for children of that age range. That COVID-19 was in the top ten causes of death for young children sounds as though a lot of children must have died from it. So, the point was to alarm parents about the threat of COVID-19 enough to have their children vaccinated as soon as the vaccine was approved.

Unsurprisingly, some news media parroted Walensky's alarming claim without any skepticism or apparent fact-checking3. However, skepticism of the claim is warranted: one thing that is known about COVID-19, and has been known since early in 2020, is that it discriminates based on age. The older you are, the more likely it is to kill you, and very young children are at minimal risk of death4.

Before we look at the top ten list in depth, let's ask a few preliminary critical questions about it. Suppose that COVID-19 were among the top five causes, would Walensky have said that it was in the top ten? Probably not, so we can conclude that the disease must be at number six at the highest on the list, and it might even be as low as ten5. So, that means that there are at least five causes that kill more children than COVID-19. Thankfully, young children who survive infancy are usually healthy and rarely die of diseases, so what are five causes that kill them at numbers greater than COVID-19? An obvious one is accidents, especially car accidents, but also accidental drownings and accidents in the home, such as fires. It's difficult to think of any diseases that kill a large number of young children, at least in the United States.

This thought raises another question: how are these different causes categorized? For instance, given that a large proportion of child deaths occur in accidents, will there be a single category of "Accidental Deaths", or would the category be broken down into "Automobile Accidents", "Accidents in the Home", or other more specific categories, such as "Accidental Drowning" or "Death in a Fire"? How fine-grained the analysis is will affect how far down the list COVID-19 ends up. So, a little critical thought shows that we should not be too alarmed by the top ten claim until we look into the details of the list of causes―let's do that now.

Apparently, the claim was based on the following table that was presented in the committee meeting that Walensky referred to6:

Leading Causes of Death in Children 5-11 Years of Age, NCHS, 2019

The table shows the ten "leading" causes of death for children from five to eleven for 2019, that is, prior to COVID-19. The COVID-19 "associated" deaths for children of the same age for the year from the beginning of October 2020 to the same time in 2021, just prior to this table being prepared, tied with the eighth leading cause of death. As you can see, the cause of death it tied with is―yikes!―suicide. You read that right: suicide in children less than twelve years old. So, COVID-19 killed in a year's time as many children as committed suicide in 2019. Thankfully, this was only 66 children, or one in a half-million―see the crude rate in the table.

Of course, every death of a young child is a tragedy, but the death of a young child by suicide is especially tragic since it should be preventable. It's only common sense that many of the steps that have been taken during the epidemic―such as school closures, distance learning, and mask wearing―are likely to harm the mental health of children. Moreover, there is already evidence of such harmful effects: for instance, emergency room visits for mental health problems increased by 24% for children 5-11 years old in the latter part of 2020 as compared to 20197.

Another factor, which is not explicitly represented in the top ten chart, is the effects of drug abuse. Deaths from overdoses of illegal drugs have increased over the last two years8. How much of this increase is due to the social and economic effects of the reaction to the epidemic is impossible to say, but it is surely not zero. Now, you wouldn't expect 5-11 year olds to die from drug overdoses, but you also wouldn't expect them to commit suicide. There is no separate category in the chart for drug deaths, so where would they fit: perhaps under "Accidents"? Or, were there so few that they would not be considered a "leading" cause of death?

I point this out because the chart makes no effort to quantify the number of deaths due to the effects of our social and economic reaction to COVID-19 on the mental health of children. Did more children die from those effects than died from COVID-19? From this chart, we simply can't tell.

To be fair to Walensky, immunization against COVID-19 probably has little if any direct effect on suicide or drug abuse among children. However, fomenting fear that COVID-19 threatens young children may contribute to the social hysteria that leads to schools being closed, children being isolated from friends and family, or forced to wear masks for long periods of time. Such actions are not good for the mental health of children, or adults for that matter.

Good intentions do not excuse presenting misleading claims aimed at scaring people into doing something even if it is the right thing to do. Walensky's top ten claim is typical of so much of public communication by government health officials: it's not an outright lie, but it is a half-truth intended to manipulate people into taking the action desired by the government. I hate to say it, but Walensky and other public health officials seem not to trust the American people with the truth. It's hard to see why the American people should trust them in return9.


  1. "FDA Authorizes Pfizer-BioNTech COVID-19 Vaccine for Emergency Use in Children 5 through 11 Years of Age", U. S. Food & Drug Administration, 10/29/2021
  2. "Press Briefing by White House COVID-19 Response Team and Public Health Officials", The White House, 10/27/2021
  3. For instance:

    A couple of exceptions at least offered some context rather than just repeating Walensky's claim:

  4. German Lopez, "How the risk of Covid-19 for kids compares to other dangers", Vox, 10/7/2021
  5. This is an application of Paul Grice's first conversational maxim of quantity, which enjoins one to be as informative as possible; see: Paul Grice, "Logic and Conversation", in Studies in the Way of Words (1989), p. 26
  6. Fiona Havers, "Epidemiology of COVID-19 in Children Aged 5–11 years", Centers for Disease Control and Prevention, 10/26/2021
  7. Rebecca T. Leeb, et al., "Mental Health–Related Emergency Department Visits Among Children Aged <18 Years During the COVID-19 Pandemic—United States, January 1–October 17, 2020", Centers for Disease Control and Prevention, 11/13/2020
  8. "Overdose Deaths Accelerating During COVID-19", Centers for Disease Control and Prevention, 12/18/2020
  9. Michael S. Pollard & Lois M. Davis, "Decline in Trust in the Centers for Disease Control and Prevention During the COVID-19 Pandemic", RAND Corporation, 2021

February 12th, 2022 (Permalink)

The Absent-Minded Professors

As I mentioned in a previous account of a meeting at the New Logicians' Club*, Professor Knight, one of its members, was notoriously absent-minded. At the most recent meeting, Knight suddenly arose from the table he shared with three other professors and dashed for the door. Apparently, he had just remembered some other appointment, as he was wont to do. Since it was cold outside, everyone had worn a coat and hat to the meeting, and these articles of apparel were hanging from a row of hooks near the entrance. In his rush, Knight grabbed a coat belonging to one of the other members at his table, and a hat belonging to a different table-mate.

As a result of Knight's mistake, when the time came for the other three members to leave, no one got the right coat and hat. In fact, each of the four members ended up with one of the other four's coat, and a hat belonging to yet another.

For some reason, Professor Knight called me up when he discovered his error. "I accidently took Professor X's hat!" he told me. "I recognize it because it's an odd-looking hat, which is probably why I grabbed it, but I don't know whose coat I got―it's certainly not mine!" As mentioned previously, Knight is an unusually honest fellow, so you can trust what he said to be true.

I promised Knight to investigate the incident and try to determine who got whose hat and coat, and arrange to return them to their rightful owners. My investigation revealed only one further clue: Professor Y's coat had been taken by the same professor who had taken Professor Z's hat.

Can you help me solve the mystery of the mixed-up hats and coats? Whose hat and whose coat had each of the four professors taken?

*Christmas at the New Logicians' Club, 12/25/2021

February 4th, 2022 (Permalink)

Credibility Checking, Part 2: Divide & Conquer

Part 11 of this series on credibility checking dealt with how to use what you know to compare and contrast with what you don't know in order to check factual claims for credibility. This part concerns how to cut big numbers down to size so that they can be easily evaluated.

Big Numbers

Many of the factual claims that you meet involve numbers, and many of those numbers will be large. This is because politicians, activists, reporters, and advertisers love big numbers. What better way to get you excited enough about something to take action, whether it is voting for a candidate, writing a check to a charity, or buying a product, than to impress you with a big number. The news media and advertisers love big numbers because they attract people's attention, and attention is money.

Unfortunately, very large numbers are often beyond our ability to understand or put into perspective, since most of us have little if any experience with them. Big numbers can cause "number numbness"2, which is the lack of a sense of their comparative magnitudes: millions, billions, trillions are all just "really big". From the standpoint of those who use big numbers to manipulate you, number numbness is a good thing since it prevents you from skeptically evaluating their claims.

Another Example

Last month, we examined in detail an example of the use of a big number by activists and politicians to alarm Americans about abducted children3. Let's look at an example where an even larger number was used to concern people about a different social problem.

A book published in 1991 claimed: "Each year, according to the association, 150,000 American women die of anorexia.4" 150,000 is a big number, especially in the context of anorexia deaths, but is it a credible number? The book claimed that the source of the number was the American Anorexia and Bulimia Association, which seems to be a credible source that ought to know.

In Part 1, we checked the credibility of the factual claim that 50,000 American children had been kidnapped by strangers in 1982. 50K is a big number, at least in the context of kidnapped children, and we compared and contrasted it with a number of the same order of magnitude (OoM), finding it implausible. 150K is, of course, three times larger and we could apply the same analysis to it, finding it three times as implausible. However, in this part, I want to use the new example to demonstrate a new technique.

As we saw in Part 1, you already know a lot, perhaps more than you realize. While you probably don't know the number of women who die from anorexia each year, you probably do have some idea of the number of people who die in car crashes, or the population of the country, or some other fact that can be put to use. Similarly, while you probably don't know the national statistic, you're more likely to have a sense of the size of the problem in your own state or local community. The problem is to bring what you know to bear on the big number by cutting it down to size.


How can you make a number that is too large to grasp easier to understand? Make it smaller. One technique to do so is to use division; of course, you have to find some appropriate way of dividing the number up into smaller numbers.

One reason that the number of supposed anorexic deaths is so big is that it's for the entire country. You can divide statistics for the entire nation by fifty in order to get the approximate number in your state, assuming that you live in the United States. In the case of the example, you can do this in your head: divide 150K by 50 to get 3K. Is it believable that three thousand women die annually of anorexia in your state?

We're not done dividing yet, since there's another dimension that we can use to divide: time. Since, according to the claim we're checking, there are an average of 3K women who die of anorexia in your state each year, we can divide by 365―a landmark number5 that we all know. This is another calculation that you can do in your head: the number of days in the year is approximately 300, which is one-tenth of 3K, which means about ten deaths a day. More precisely, the result of dividing 3K by 365 is slightly more than eight, but keep in mind that a ballpark estimate is all that we need.


Now, having divided the big number in about every way that makes sense, you're in a position to apply what you know to it. Is it plausible that eight or ten women die every day in your state from anorexia? Have you seen reports in your state's news media about an epidemic of anorexic deaths? I can't answer these questions for you, but I can say that it is highly implausible that there could be so many deaths in my state without my having heard a word about it.

Dividing and conquering suggests that the factual claim that 150K American women die each year from anorexia is quite implausible. As we saw in Part 1, the number of Americans of all ages and both sexes who die in automobile accidents yearly is around 30-35K, that is, four to five times less than the supposed number who die from anorexia, which would mean that anorexia was four to five times worse a problem than traffic fatalities, at least in terms of deaths. I find it hard to believe that such a large problem would receive so little attention.

Of course, sometimes surprisingly implausible claims are true. Keep in mind that the point of a credibility check is not to decide whether a factual claim is true or false, but to decide whether it is worth fact checking. This example clearly is worth checking.

Fact Check

Thankfully, I don't need to do a full fact check of this claim since I did one ten years ago6: check it out if you want the full details. The gist is that the actual number of anorexia deaths per year in the United States is in the tens or hundreds, not tens or hundreds of thousands. Thus, the claim was wrong by three or four OoMs.

I hope that this entry convinces you not to be intimidated by large numbers, since now you know how to cut them down to size. Also, you shouldn't be discouraged by your own ignorance. Before reading this entry, you probably didn't know even approximately how many people die of anorexia each year. However, you do know many things that you can use to check the credibility of claims about what you don't know.

As we've seen, you can't always trust claims made by politicians, activists, or books, so the next time you come across such a claim that uses a big number, divide and conquer!


  1. Credibility Checking, Part 1: Compare & Contrast, 1/7/2022.
  2. Douglas R. Hofstadter, "On Number Numbness", Metamagical Themas (1985), pp. 115-135.
  3. The Goldilocks Number, 1/23/2022.
  4. Naomi Wolf, The Beauty Myth: How Images of Beauty are Used Against Women (1991), pp. 181-182.
  5. A landmark number is one that helps you find your way around the data landscape and is, therefore, worth remembering.
  6. Be your own fact checker!, 2/15/2012

February 2nd, 2022 (Permalink)

Tenet or Tenant?

I recently came across an example of the word "tenant" used in place of "tenet", but I haven't been able to find it again. It reminded me that I had seen previous cases in which the two words were confused. Here's one I was able to find in an abstract of a paper published in a medical journal: "Although the pathophysiology of edema varies, compression therapy is a basic tenant of treatment, vital to reducing swelling.1"

"Tenet" and "tenant" are similarly spelled, and their pronunciations are even similar, especially when people don't enunciate clearly. Yet, the two words are very different in meaning, though both are nouns. A "tenant" is someone who rents a place, whether an apartment or farmland2, whereas a "tenet" is a principle or axiom of a religion or other system of belief3. Because of their similar spelling and pronunciation, "tenant" is occasionally written when "tenet" is meant, as in the above example. The mistake seems to seldom if ever go in the opposite direction, perhaps because "tenet" is a less familiar word, and I don't recall ever seeing "tenet" in place of "tenant".

For another possible example, the online Cambridge Dictionary supplies the following as an example of the use of the word "tenant": "Not entirely unexpectedly, the articulation by some of self-concept/image entailed express or implied criticisms of tenants.2" It's a confusing sentence, and the dictionary does not supply a citation or any further context that might help to clarify it. Still, to the extent that it makes any sense at all taken out of context, it seems to make more sense if we suppose that "tenets" was meant in place of "tenants". If so, this is not an example of the use of the word "tenant", but of its misuse.

Somewhat to my surprise, none of the reference works I usually consult discuss the confusion of "tenant" for "tenet", which suggests that it isn't such a common mistake. However, the online Merriam-Webster dictionary does have a page about it, and supplies a couple of clearer examples4.

Given that both words are English nouns, it's unlikely that a spell-checker or even a grammar-checker will catch the substitution of one for the other. I tried one or more examples in my old copy of Microsoft Word, and an online grammar-checker, neither of which noticed any problems with them.

One of the basic tenets of the use of spell- and grammar-checking programs is that they will catch most mundane typographical errors, freeing up your memory for the kind of mistakes that the programs themselves won't prevent. So, file the difference between "tenet" and "tenant" in your mental spell-checker.


  1. N. Stout, et al., "Chronic edema of the lower extremities: international consensus recommendations for compression therapy clinical research trials", Int Angiol., 2012 Aug;31(4):316-29.
  2. "Tenant", Cambridge Dictionary, accessed: 2/2/2022.
  3. "Tenet", Cambridge Dictionary, accessed: 2/2/2022.
  4. "On 'Tenant' vs. 'Tenet'", Merriam-Webster, accessed: 2/2/2022.

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